So you're having the issue with Apex Launcher, not TouchWiz icon?
The code in Aqua to send unread counts to Apex is pretty much unrelated to TouchWiz integration code.
However, when you turn the TouchWiz setting off an on, Aqua will re-send the unread counts to all launchers, Apex, Nova, Samsung, LG, Sony.
I keep hearing about issues with Apex from time to time, but every time I try to reproduce (installing latest Apex from Play, as I normally use only standard system launchers on all my devices) -- it works just fine.
Now, since there is a time factor -- could you capture the issue in a debug log, and note the time when the count goes wrong (and when you re-set it), so I could know where to look?